Goldanskii—Karyagin effect

In anisotropic crystals, the amplitudes of the atomic vibrations are essentially a function of the vibrational direction. As has been shown theoretically by Karyagin [72] and proved experimentally by Goldanskii et al. [48], this is accompanied by an anisotropic Lamb-Mossbauer factor/which in turn causes an asymmetry in quadra-pole split Mossbauer spectra, for example, in the case of 4 = 3/2, f = 1/2 nuclear transitions in polycrystalline absorbers. A detailed description of this phenomenon, called the Goldanskii-Karyagin effect, is given in [73]. The Lamb-Mossbauer factor is given by... 

NFS spectra recorded at 300 K for -cut and c-cut crystals are shown in Fig. 9.17 [48]. The/factors for the two orientations were derived from the speed-up of the nuclear decay (i.e., from the slope of the time-dependent intensity in Fig. 9.17a and from the slope of the envelope in Fig. 9.17b). The factors obtained f ( P = 0.122 (10) and f = 0.206(10) exhibit significant anisotropic vibrational behavior of iron in GNP. This anisotropy in f is the reason for the observed asymmetry in the line intensity of the quadrupole doublet (in a conventional Mossbauer spectrum in the energy domain) of a powder sample of GNP caused by the Goldanskii-Karyagin effect [49]. 

The other possible reason for the intensity asymmetry (A2M1 1) of the quadrupole split doublet can be the so-called Goldanskii-Karyagin effect (Goldanskii et al. 1963), which is caused by the angular dependence of the Mossbauer-Lamb factor due to the anisotropy of lattice vibrations (jf(0) depends on 0). 

For a comparison of the Goldanskii-Karyagin effect with the effect of texture see, e.g., Pfannes and Gonser (1973). 

The purpose of this chapter is to review the application of Mossbauer spectroscopy to the study of dynamics. The main emphasis will be on the new areas in which significant advances have been made in recent years, such as the study of diffusive processes, the influence of motion on lineshape, time-dependent studies and dynamics at phase transitions. Rather less attention will be devoted to areas such as /-factors in solids, the Goldanskii-Karyagin effect and temperature shift, which have been studied more extensively in the past. The trends towards future areas for this research will also be considered, together with an evaluation and comparison between Mossbauer spectroscopy and other methods for investigating these phenomena. 

Information about the bond strength of the If/ If anions in the (CH) matrix can be obtained by measuring the absorption strength (/-factor) in oriented samples as well as the temperature dependence of the /-factor and of the Goldanskii-Karyagin effect (GKE) in non-oriented samples. We performed such studies on non-oriented S-(CH1 ) ,. samples, applying both I and I resonance. Typical spectra are shown in Figure 3.11. 

Fig. 11. Quadrupole hyperfine spectrum of Np in Np metal. The bar diagram shows the decomposition into two quadrupole patterns meaning that Np occupies two lattice sites with different local symmetries. In both cases the electric field gradient is not rotationally symmetric (rj 0). The fit (solid line) includes the Goldanskii-Karyagin effect (see text). The dashed line shows the spectrum expected in case of full isotropy. [Taken from Dunlap et al. (1970).]...

In general one needs to take into account the dependence of phonon excitation on the direction of the recoil momentum of the nucleus with respect to the crystallographic axes. This must be considered in particular when strong anisotropy is observed for laminar crystals. The anisotropy factor f that is detected for some nontextured polycrystalline samples takes this into account in a phenomenon known as the Goldanskii-Karyagin effect. 

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